Question

if 12th term of an apbis -13 and the sum of first four term is 24 what is sum of first 10 term?

Answer 1

given, 12th term is -13
i.e a₁₂=a₁+11d (a₁ is first term and 'd' is common difference)
Let, the first four terms of A.P is a,a+d,a+2d,a+3d
Given, sum of first four terms is 24
Then, a+(a+d)+(a+2d)+(a+3d)=24
        4a+6d=24
    or 2a+3d=12 (equation 1)

a₁₂=a₁+11d
-13=a₁+11d (equation 2)
On solving equation 1 and 2 , we will have
d= - 2
therefore, putting d= - 2 in equation 2 we will have a₁=9(first term)

a₁₀=a₁+9d
    =9+9(-2)
    = -9 (last term as per question)

Sum of ten terms is:
Formula is S₁₀= n/2 (first term + last term)
                     = 10/2 (9+(-9)
                     = 0 (zero)